A graph of y=f(x) is shown, where f(x)=2x^5-3x^4+x^3-8x^2+5x+3 and f(-x)= -2x^5-3x^4-x^3-8x^2-5x+3. a.  How many negative real zeros does f have?  Explain.   b.  How many positive real zeros are possible for f?  Explain.  What does this tell you about the eventual right-hand behavior of the graph?   c.  Is x= -1/3 a possible rational zero of f?  Explain.   d. Explain how to check whether (x - 3/2) is a factor of f and whether x=3/2 is an upper bound for the real zeros of f.

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: Rewrite each expression as a polynomial in standard form. a. (2x -x -9x +1)- (x+7x-3x + 1)

A: Given. We are given a polynomial and we need to convert it in standard form. We need to add all the…

Q: . the function x^4 -2x^3 -6x^2 + 22x -15 = 0 has how many roots? part 2. list all the zeros of the…

A: Here we have to find the roots of the equations.

Q: Find all zeros of the polynomial function f(x) = -(x - 2)2(x + 1)2.Then graph the function.

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Q: 2 9 x - x = (x)} JI a. Write f(x) in vertex and intercept form b. Find the maxima c. Write the…

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Q: 9. (a) Show that the functions r(t) = 3et+ 7e-t and y(t) = 3et+ 21e are solutions of the system I' =…

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Q: what is a cubic plolynomial function in standard form with zeros -4, -5 and 4 a.…

A: given zeros -4,-5 and 4

Q: determine whether  the following numbers are roots of the polynomial equation P(x) = 0, P(x) =2x^3 -…

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Q: 4x

A: Zeros of f(x) must satisfy f(x),i.e., f(x) will reduce to zero at the zeros of f(x).

Q: Sketch y=-3(x-1)^(2)(x+2), making sure to account for end behavior along with zeros and their…

A: y=-3(x-1)^(2)(x+2)

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Q: Let f (x) = 5* – 7x - , for what value of root that the relative error would be equal or less than…

A: Given that f(x)=5x-7x2 The newton method formula is, xn+1=xn-f(xn)f'(xn) Take the derivative for f,…

Q: A young boy shoots a rocket off of a table and the height of the rocket in meters is given by h(t) =…

A: Here we have to find the time and height.

Q: Divide the polynomials using synth (2x^(3)-22x^(2)+57x-7)-:(x-7)

A: Given  polynomial , 2x3-22x2+57x-7 Divide by x-7

Q: Given the function y = f(x) = (x − 2)(x + 5)(x-7) ts y-intercept is Give the y-intercept as an…

A: The given function is

Q: Determine the end behavior of the polynomial: P(x)= -x^7+x^3-x-1 Step by step please please

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Q: Find the zeros of f(x) = x^2 − 6x + 10. Then, compute x1/x2 where x2 is the zero with positive…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.